Variable and Orbital-Dependent Spin-Orbit Field Orientations in an InSb Double Quantum Dot Characterized via Dispersive Gate Sensing

Abstract

Utilizing dispersive gate sensing (DGS), we investigate the spin-orbit field (${\mathbf{B}}_{\mathrm{SO}}$) orientation in a many-electron double quantum dot (DQD) defined in an $\mathrm{In}\mathrm{Sb}$ nanowire. While characterizing the interdot tunnel couplings, we find the measured dispersive signal depends on the electron-charge occupancy, as well as on the amplitude and orientation of the external magnetic field. The dispersive signal is mostly insensitive to the external field orientation when a DQD is occupied by a total odd number of electrons. For a DQD occupied by a total even number of electrons, the dispersive signal is reduced when the finite external magnetic field aligns with the effective ${\mathbf{B}}_{\mathrm{SO}}$ orientation. This fact enables the identification of ${\mathbf{B}}_{\mathrm{SO}}$ orientations for different DQD electron occupancies. The ${\mathbf{B}}_{\mathrm{SO}}$ orientation varies drastically between charge transitions, and is generally neither perpendicular to the nanowire nor in the chip plane. Moreover, ${\mathbf{B}}_{\mathrm{SO}}$ is similar for pairs of transitions involving the same valence orbital, and varies between such pairs. Our work demonstrates the practicality of DGS in characterizing spin-orbit interactions in quantum dot systems, without requiring any current flow through the device.